What is the normal period for tangent and cotangent functions?

The normal period for tangent and cotangent functions is π. This is because the tangent function, which can be defined as the ratio of sine to cosine, completes one full cycle every time the angle increases by π radians. This is evident when you consider the unit circle: as you move through π radians, the tangent function will return to the same value at both endpoints because the sine and cosine values will repeat in a cycle.

For the cotangent function, which is the reciprocal of the tangent function, the same reasoning applies. It is also periodic with a period of π. As cotangent is dependent on sine and cosine, it, too, resets every π radians.

The essential characteristic of both functions is that they contain vertical asymptotes whenever the cosine function (for tangent) or sine function (for cotangent) equals zero, which occurs at these intervals, reinforcing that the total span of one complete cycle is indeed π.

The other options do not represent the periods of the tangent and cotangent functions. The 2π period applies to sine and cosine functions, while π/2 and 3π do not correspond to the repeating nature of the tangent or cotangent behavior. Therefore, recognizing the properties of these functions related to angles on the